S\'eries discr\`etes des espaces sym\'etriques et paquets d'Arthur

Abstract

We check Sakellaridis-Venkatesh conjectures giving a description of the discrete spectrum of a spherical variety $\mathscr{X}=G/H$ in the Langlands-Arthur formalism when $G$ is a classical real group and $\mathscr{X}$ is a symmetric space. Then, we compute explicitly the representations in the relevant Arthur paquets which appear in the discrete spectrum, and we establish some multiplicity one results.